TL;DR: Get rid of the current competition system. Replace it with two separate comps, one which is judging/feedback ONLY (no winning awards) and another which is ONLY awards, but with no categories. BOS-type stuff.
Sounds like you might be due for a local brewclub meeting.... I doubt many people would invest any time to submit a beer or participate in that idea.
I'm founder & president of the Paris Homebrewers Club, so I attend every meeting. And funny enough, this is exactly the sort of comp structure we use.
Under the homebrew club umbrella that's pretty typical thing to have going on - and hats off to your club for doing that.... Anyone who is/has been in a homebrew club usually grows tired of having their beer judged in that environment and wants something more. Nationally it won't work especially when you consider the costs and time for something like that.